An object moving in $\mathbb R^2$ with a high-speed destructive miniobject and an unfriendly solid observer

V. I. Berdyshev

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 26 (2020) no. 4, pp. 76-82

Résumé

We propose a model for the motion in a given corridor $Y\subset \mathbb{R}^2$ of an object $t$ equipped with a high-speed destructive miniobject in the presence of a solid unfriendly observer $f$. In $\mathbb{R}^2\backslash Y$ there is a subset $G$ that obstructs visibility and motion. For safety reasons, the observer sticks to neighborhoods of the angles and convex fragments of the boundary of $G$. The trajectory of $t$ is a curve $\mathcal{T}\subset Y$ with a given speed regime $v_t$ of the motion along it. The possibilities for the observer to track the object in a safe mode and for the object to avoid the observation depend on the positions of the observer and the object. We characterize the positions in which, for any $\mathcal{T}$, the object can choose a regime $v_t$ enabling the avoidance of observation and the positions guaranteeing that the observer can see a part of the trajectory.

Détail

Mots-clés : navigation, observer
Keywords: trajectory, moving object.